Bulging Garden Hose Animation
The cast modifier should let you do exactly what is in the video, with only a couple of steps.

To set it up, you will need a hose object with fairly dense geometry, and an object to pass through the hose.

To set up the system, you will need to have the object (I'm going to use a sphere as an example since that was the object in the video) positioned at one end of the hose, and animated to move through it. I would think a curve would be the best way to animate the object, and you could also use the same curve to bend the hose.

Once you have the animation set up, simply add a cast modifier to the hose, select the sphere in the control object box and then adjust the radius until the hose completely covers the object.